CFD-PBE Modelling and Simulation of Enzymatic Hydrolysis ... · Enzymatic hydrolysis of cellulose is a complex phenomenon. It consists of several effects that occur simultaneously

© 2016 Norazaliza Mohd Jamil and Qi Wang. This open access article is distributed under a Creative Commons Attribution

(CC-BY) 3.0 license.

Journal of Mathematics and Statistics

Original Research Paper

CFD-PBE Modelling and Simulation of Enzymatic Hydrolysis

of Cellulose in a Stirred Tank

1Norazaliza Mohd Jamil and

2Qi Wang

1Faculty of Industrial Sciences and Technology,

Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan, Pahang, Malaysia 2Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208, USA

Article history

Received: 28-07-2016

Revised: 28-09-2016

Accepted: 22-10-2016

Corresponding Author:

Norazaliza Mohd Jamil

Faculty of Industrial Sciences

and Technology,

Universiti Malaysia Pahang,

Lebuhraya Tun Razak, 26300

Gambang, Kuantan, Pahang,

Malaysia Email: [email protected]

Abstract: Renewable energy or biofuel from lignocellulosic biomass is an

alternative way to replace the depleting fossil fuels. The production cost can

be reduced by increasing the concentration of biomass particles. However,

lignocellulosic biomass is a suspension of natural fibres and processing at

high solid concentration is a challenging task because it will affect the

mixing quality between the enzyme and cellulose particles and the

generation of sugars. Thus, understanding the factors that affect the

rheology of biomass suspension is crucial in order to maximize the

production at a minimum cost. Our aim was to develop a solution strategy for

the modelling and simulation of biomass suspension during enzymatic

hydrolysis. The complete model was solved using the DAE-QMOM

technique in a finite-element software package, COMSOL. Essentially, we

made a clear connection between the microscopic and macroscopic properties

of biomass slurries undergoing enzymatic hydrolysis. The results showed

that the quality of mixing within a reactor is crucial in optimizing the

hydrolysis product. The model improved the predictive capabilities, hence

increasing our understanding on the behaviour of biomass suspension.

Keywords: DAE-QMOM, PBE, Enzymatic Hydrolysis, Cellulose, Biomass

Introduction

Enzymatic hydrolysis of cellulose is a complex

phenomenon. It consists of several effects that occur

simultaneously in a biomass suspension reactor, such as

fragmentation of cellulose chains, in homogeneity in the

tank, mixing effect and adsorption of enzymes to the

cellulose substrates. In fact, even though numerous

issues have been explored, they cannot be considered as

fully covered.

It was discovered that advection did represent a

significant phenomenon that could increase the number of

cellulose particles generated during the hydrolysis process.

Besides advection and the diffusion factor, another critical

aspect in the enzymatic hydrolysis of cellulose for

bioethanol production is the contact between the enzymes

and the cellulose substrates (Jager and Buchs, 2012). The

problems that arise at present are very low solubility of

cellulose substrates and as for the economic issue; costly

high enzyme concentrations are commonly applied. Hence, this paper depicted the development of a

solution strategy in resolving the modeling, as well as

the simulation of the PBE-advection-diffusion system,

coupled with a fluid medium surrounding the cellulose

particles. The cellulose particles were suspended in a

continuous fluid that was assumed to obey the

incompressible Navier-Stokes equations. Besides, the

mixing between biomass suspension and cellulase

enzymes was simulated in a cylindrical stirred tank,

mechanically agitated by a stirrer. In addition, the

influence of the mixing speed of the stirred tank and

different locations of enzyme injection points in the

mixer to the hydrolysis yield were investigated

numerically. Meanwhile, the model of Griggs et al.

(2012a) for the hydrolysis of cellulosic biomass was

extended and modified to accommodate the

Computational Fluid Dynamics (CFD), which led to

strong spatial in homogeneities in the flow and the

species concentration fields. Furthermore, the capability

of DAE-QMOM approach (Gimbun et al., 2009) was

tested to solve the coupled model. Many theoretical and experimental studies have

been described in the literature, trying to capture the important aspects of the enzymatic hydrolysis process (Abnisa et al., 2011; Bansal et al., 2009; Carvajal et al., 2011; Fan and Lee, 1983; Griggs et al., 2012a; 2012b;

Norazaliza Mohd Jamil and Qi Wang / Journal of Mathematics and Statistics 2016, (): .

DOI: 10.3844/jmssp.2016..

Himmel et al., 2007; Igarashi et al., 2009; Kleman-Leyer et al., 1996; Limayem and Ricke, 2012; Okazaki and Moo-Young, 1978; Selig et al., 2008; Srisodsuk et al., 1998). From these studies, several kinetic models based on discrete and continuous formulations on population balance equations had been proposed. However, to the best of our knowledge, the coupling of enzymatic hydrolysis kinetic model with fluid dynamic has not been reported. Nevertheless, the Standard Method of Moments (SMM) and Quadrature Method of Moments (QMOM) had been employed in conjunction with CFD to simulate the process of precipitation of barium sulfate (Cheng et al., 2009). In another study, Marchisio et al. (2003) implemented the QMOM in a CFD code FLUENT in modeling simultaneous aggregation and breakage problem.

This paper is organized as follows. First, the

development of phase-space kinetic is illustrated for

the model formulation. Next, in the third section, the

setup of the 2-D stirred tank simulated in COMSOL is

presented. Besides that, the mixing in the stirred tank

is discussed and then, the results and discussion are

provided by using the model developed in this study.

Finally, a conclusion of this paper is given. This study

is expected to provide a valuable insight concerning

the features of the breakage phenomena during the

enzymatic hydrolysis of cellulose in a stirred tank.

Phase-Space Kinetic Model

The population balance for the enzymatic hydrolysis

of cellulose problem was originally expressed in terms of

the number of the density function, p(χ, t) with the

particle length χ as its internal coordinate (Griggs et al.,

2012a). The PBE describes how the particle size

distribution changes as time progresses due to polymer

breakage during cellulosic hydrolysis. Furthermore, it is

assumed that the fluid environment plays an explicit role

in particle behavior. In this case, the distribution of

particles depended not only on internal coordinates, but

also on its location in the physical space, referred to as

external coordinates, x, here. The external coordinate

was utilized to locate the physical positions of suspended

cellulosic particles, which were governed by flow

advection and particle diffusion (Ramkrishna, 2000).

From these coordinates, the PBE for an enzymatic

hydrolysis process can be governed by:

( )( ) ( )

( )( ) ( )

( )( )

, ,

, , , ,

, ,

, , , ,

,

, , , ,

B B B B

p B p

pB

Bp p p p

R

R B R

p x tf p p R t u p D p

t

x tf p p R t u D

t

x tf p p R t u

t

χχ

χχ

χ

∂= − ⋅∇ +∇ ⋅ ∇

∂∂

= − ⋅∇ + ∇ ⋅ ∇∂

∂= − ⋅∇

∂

(1)

where, u is the mean velocity vector, Dp and DpB are the

particle diffusion constants for the length χ of p and pB,

respectively. Here, p denotes the population distribution

of enzyme-accessible cellulose chains of length χ, pB is

the population distribution of CBH1-threaded cellulose

chains of length χ and R is the radius of the cellulose

particles. The source terms fp, fpB and fR represent the

reaction terms due to the breakage process by EG1 and

CBH1 enzymes of the cellulose chains, which are given

respectively by:

( )( )

( ) ( )

( )

( )

( )

( )

( )

( )

1 (1)(0)

(1) (1)

1 (1)

(1) (1)

1 (1)

(1) (1)

1 (1)

(1) (1)

, , , ,

,

0.004 ,

0.002 ,

0.002 ,

P B

CBH CBHBf T BCBH

B d

EG EGBh TEG

B d

EG EGBh TEG

B d

EG EGBh T BEG

B d

f p p R t

p Pk E p p t

p P K

p pk E p y t dy

p P K

p pk E p t

p P K

p pk E p y t dy

p P K

R R

χ

χ

χ

χ

χ χ

∞

∞

=

+− −

+ +

++

+ +

+−

+ +

++

+ +

−−

∫

∫

ɶ

ɶ

ɶ

( )( )

(1) (1)

002

0 0

,2

BB

dp dpp p R R

dt dtR nL R Rρπ

+ + ≥

−

(2)

( )( )

( ) ( )

1 (1)

(1) (1)

(0)

2 2

22 2

, , , ,

,

2

B

B

CBH BB f CBHp

B d

CBH

T B

pCBH Bh

p Pf p p R t k

p p K

E p p t

x pk x

χ

χ

χ χ

+= −

+ +

−

∂ ∂ + +

∂ ∂

(3)

( )

( )1 (1)

(1) (1)0.002 ,

EG EGB

h T BEG

B d

p pk E p y t dy

p P K χ

∞+

+

+ +∫ɶ (4)

( )

( )1 (1)

(1) (1)0.002 ,

EG EGB

h T BEG

B d

p pk E p t

p P Kχ χ

+

−

+ +

ɶ (5)

( )( )1

(1)

0

0

1, , , , ,

2

B

R B

dp dpf p p R t R R

nLR dt dtχ

ρπ

= + ≥

(6)

The equations in (1) are the integro-partial

differential equations, which describe how the dispersed

phase evolves in time, space and size coordinates. The

problem apparently became more complicated when

external coordinates appeared in the models. Hence, we

nondimensionalized the system so as to reduce the

number of parameters involved and to make the

equations compact.

The Method of Moments (MOM) was first

introduced by (Hulburt and Katz, 1964) and it forms


DOI: 10.3844/jmssp.2016..

the basis for many promising solution strategies. The

basic idea of MOM is to transform the original PBE

into a problem in identifying the moments in size

distribution. However, applying the definitions of

moments to the reduced model equations results in a

closure problem for the system.

Therefore, a practical approach to solve the closure

problem is the QMOM, introduced by (McGraw, 1997).

In QMOM, the integral terms containing the size of the

distribution function are approximated by numerical

quadratures in the same fashion as in numerical

integration. With this approach, the moments can be

expressed as:

( ) ( ) ( ) ( )1

, , ,

nqkk

i i

i

p x t w x t x tξ=

=∑ (7)

and:

( ) ( ) ( ) ( )1

, , ,

nqkk

B i i

i

p x t e x t L x t=

=∑ (8)

where, nq is the order of the quadrature formulation, ξi

and Li are the particle lengths, while wi and ci are the

quadrature weights for p and pB, respectively. About

60 Accordingly, p(0) is the total number of enzyme

accessible cellulose particles and p(1) is the total

number of monomeric glucans for enzyme accessible

cellulose particles.

Subsequently, by combining the algebraic equations

from the QMOM definitions and the partial differential

equations from the moment transport equations, the

Differential Algebraic Equations (DAE) system was

obtained. This method is known as the DAE-QMOM

method, proposed by (Gimbun et al., 2009). Therefore,

the full system can be expressed as:

( ) ( ) ( )

( )( ) ( )

( )

( ) ( )

( )

0

( )

( )

( )

0

( )

1

( )

1

,

, , , ,

,

, , , ,

,

0

0

B B

k

k

p

k k

p p B

k

B k

B

k k

B Bp p

R

nqk k

i i

i

nqk k

i i B

i

p x tu

t

D p f p p R t d

p x tu p

t

D p f p p R t d

R x tu R f

t

w p

e L p

χ χ χ

χ χ χ

ξ

∞

∞

=

=

∂+ ⋅∇

∂

−∇ ⋅ ∇ =

∂+ ⋅∇

∂

−∇ ⋅ ∇ =

∂+ ⋅∇ =

∂

= −

= −

∫

∫

∑

∑

(9)

Fig. 1. Sketch of coupling effects in the model for enzymatic hydrolysis of cellulose


DOI: 10.3844/jmssp.2016..

The developed mathematical model consisted of

three parts: (i) The hydrodynamic core, a model to solve

the incompressible Navier-Stokes equations; (ii)

transport equation for advection and diffusion problems,

(iii) PBE to describe the size distribution of cellulose

particles. The schematic view of how these models are

interconnected is given in Fig. 1. The coupled phase-

space kinetic model with hydrodynamic is visualized as

a single phase laminar flow. The behavior of the fluid is

described by the incompressible Navier-Stokes equation

as portrayed below:

( ) ( )( )Tuu u pI u u

tρ ρ µ∂ + ⋅∇ = ∇ ⋅ − + ∇ + ∇ ∂

(10)

0u∇ ⋅ = (11)

where, u is the velocity vector, p is pressure, ρ gives the

fluid's density and µ denotes the dynamic viscosity. The

velocity of the laminar flow calculated from the Navier-

Stokes equations was used to solve the moment transport

equations by providing the fluid convective velocity.

Meanwhile, the reaction terms in the transport equations

consisted of quadrature weights and quadrature abscissas

variables, which can be solved with nonlinear algebraic

equations. The DAEQMOM technique that originally

solved the pure PBE problem, developed by (Gimbun et al.,

2009), had been tested in solving the coupled fluid

dynamics and population balance kinetic models for the

enzymatic hydrolysis of biomass.

Setup of 2-D Stirred Tank in COMSOL

The reactor tank simulated in this study was a

horizontal stirred mixer. The cylindrical mixing tank is

represented by a 2D schematic cross-section of a tank, as

illustrated in Fig. 2. The mixer tank was stirred by four-

blade impellers and had four equally-spaced baffles

attached to the wall to enhance mixing. The impellers

rotated clockwise at a speed of 1-9 RPM and the fluid in

the mixer consisted of biomass suspension. The cellulose

molecules were long chains of mono-saccharides and as

the fluid was non-Newtonian and viscous; Carbopol with

a density at 208 kg/m3 and viscosity at 4000Pa⋅s was

simulated as a model fluid to mimick the properties of

biomass suspension.

The geometry of the mixer was divided into two

parts: The rotating domain that formulated the Navier-

Stokes equations located in the small circle covering the

impeller; and the fixed material coordinate system was

applied on the outside ring covering the baffles. Both the

inner and the outer domains were linked to each other by

an assembly boundary, i.e., the line circle between the

impeller and the wall of the mixer. Here, the line circle

had a flux continuity boundary condition and it

transferred momentum to the fluid in the outer domain.

Fig. 2. 2D schematic cross-section of a tank with four-blade impellers and four equally-spaced baffles. The velocity field and the

flow pattern in the mixer tank are presented


DOI: 10.3844/jmssp.2016..

Besides, a no-slip boundary condition was imposed to

the reactor's fixed walls. This was consistent with no

inflow and outflow from the reactor, which was

expected. At the impeller, the convection followed the

flow, so the impeller boundaries were set to a convective

ux. Furthermore, the CFD simulation in COMSOL 4.3b

employed the following setting: Type, 2D; and Model:

Rotating Machinery Laminar Flow (incompressible

flow), Transport of Diluted Species and Domain ODEs

and DAEs. The Rotating Domains feature was applied to

specify the rotational frequency and the direction that

represented the effect of an impeller on the fluid.

Moreover, a single-phase model with PBE-advection-

diffusion, coupled with hydrodynamics, was developed

and solved with the DAE-QMOM approach within

COMSOL. It solved a momentum balance to fully

describe the stirred fluid. It also solved a material balance

to describe how the concentration distribution was

affected by the stirring. Meanwhile, the seeding of the

enzyme was done at a point in the mixer, while the mixing

between the enzyme and the fluid was monitored.

Mixing in a Stirred Tank

The impellers in a stirred tank reactor were used to

generate flow and mixing within the reactor. Mixing in

reactors is a challenging problem that has attracted

numerous studies, including experimental and

fundamental theories. The interaction of chemical

reactions and fluid mechanics can cause significant

complexity to a system (Madras and McCoy, 2004). The

efficiency of a reactor is determined by the efficiency of

the mixing within the reactor, as good mixing increases

the production process. Besides, increased fundamental

understanding of hydrodynamics and mixing in such

reactor leads to a reduction in power usage.

Moreover, several studies investigating the modeling

of fluid dynamic in a stirred tank have been carried out.

For example, (Guha et al., 2006; Micale et al., 2000)

accounted for flow description within the reactor, but

ignored the kinetic effects of the reactor performance.

On the other hand, Madras and McCoy (2004) studied

the mixing effect in a stirred tank incorporating the

population balance equations but did not take into

account the flow description within the reactor.

Therefore, in order to study the effect of hydrodynamics

on the mixing behavior, decoupling the flow and kinetics

of the system are required.

In the case of the enzymatic hydrolysis of cellulose,

the enzymes in a reactor need a sufficient contact with

the cellulose substrates before the fragmentation of

cellulose chains can take place. Hence, mixing within the

reactor is required. More importantly, mixing is

necessary to avoid areas with high concentrations of

hydrolysis products (cellobiose and glucose), which

would inhibit the enzymes (Jorgensen et al., 2007). This

is because; a good enzyme distribution is necessary to

facilitate high biomass conversion rates (Roche et al.,

2009). Consequently, the production of hydrolysis yield

can be affected by the mixing. Hence, a proper

understanding of the mixing effects in the cellulosic

hydrolysis process can lead to the reduction in cost and

increase the profitability of operation.

Apart from that, a biomass suspension, together with

a solution of enzymes, was stirred in a reactor. In the

simulation carried out in this study, the enzyme was

injected at a point inside the stirred tank reactor. Then,

the agitation of the impeller caused the enzyme to spread

to a different place in the domain. Thus, the

quantification of the mixing that varied with time in the

stirred tank had been desirable. This was done by

integrating the difference between the actual

concentration and the mean concentration throughout the

domain using the following formulation (Comsol, 2007):

( )2

meanMixingValue c c d= − Ω∫ (12)

where, c is the actual concentration and cmean is the mean

concentration. Based on Equation 12, the MixingValue

gave a relative value of how well the mixing inside the

tank was and how far it was from the ideal mixing

(Comsol, 2007). MixingValue is a key variable, which

provides a way to evaluate mixing effectiveness and to

compare the mixing systems. It provides information at

which the tank attains a specified degree of uniformity.

For the present study, the mixing of carbopol and

enzymes in a stirred tank was modeled and simulated by

using the COMSOL software. The fluid flow and the

population balance equations were coupled for the

cellulosic hydrolysis process through the DAE-QMOM

approach, in which it bridged the gap between CFD and

the phenomenological model. The goal was to predict

the influence of mixing on the production from the

enzymatic hydrolysis of cellulose. In order to do so, the

effects of the mixing speed and enzyme feeding location

on the hydrolysis yield in the system had been identified.

The conventional evaluation mixing was done through

experiments in a laboratory. This approach is usually

expensive, time-consuming and difficult. In this regard, a

valid model simulation offers a better alternative, whereby

one can examine various parameters of the mixing process

within a shorter time and at less expense. The purpose of

the present study was to evaluate the capability of

numerical simulation, i.e., DAE-QMOM, to predict

different features of the mixing process for cellulosic

hydrolysis. COMSOL 4.3b was used to solve PBE that

operated in conjunction with its flow calculations to

predict the behavior of the system. The two-dimensional

cross-sectional reactor that was constantly stirred by the


DOI: 10.3844/jmssp.2016..

movement of an impeller had been simulated. The

problem was indeed challenging since the effects of fluid

flow, transport of species and reaction kinetics had to be

included in the model simulation. Here, the biomass suspension was considered as a

single-phase laminar flow. Figure 2 displays the velocity distribution of carbopol in a stirred mixer calculated with the Navier-Stokes equation with density ρ = 208 kg/m

3

and viscosity µ = 4000Pa⋅s, as well as a mixing speed of 1 rpm. The red arrows illustrate the flow pattern of the fluid, while its length indicates if the fluid moves slowly or fast. As depicted in the figure, the fluid near the walls moved slower than the fluid in the center of the tank. In

addition, the highest velocity magnitude was located at the tip of the mixer blades.

Figure 3 shows that the number-averaged chain

length,(1)

(0)M

px

p= , decreased with time during the

hydrolysis process in the coupled PBE-advection-diffusion

with the hydrodynamics model. This result indicated that

the long cellulose chains were fragmented into shorter

ones by the actions of enzymes EG1 and CBH1, which had

been consistent with the previous findings in the earlier

chapters. Furthermore, several tests on the mixer

pertaining to the hydrolysis process were carried out.

Fig. 3. The number-averaged chain length decreased with time during the hydrolysis process in the coupled PBE-advection-diffusion

with the hydrodynamics model

Fig. 4. Glucose concentration after 3 h of cellulosic hydrolysis for initial enzyme feeding at the outer circle (circle) and the inner

circle (square) of a stirred tank at varying mixing speeds


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First, the effect of mixing speed on the hydrolysis yield was predicted. Then, the model was tested to show if the feeding location of enzymes brought any difference to the production of sugars.

Effect of Mixing Speed

On top of that, the effect of mixing speed to the

cellulosic hydrolysis yield in the stirred tank was

investigated. The simulation for various mixing speeds

i.e., 1, 3, 5, 7 and 10 rpm, was conducted for two different

enzymes feeding locations. The feeding locations were in

the outer and the inner circle of the stirred tank.

Meanwhile, Fig. 4 portrays the concentration of glucose at

0.158 mol/m3 for enzyme feeding in the outer circle, while

0.365 mol/m3 for the inner circle after 3 h at different

mixing speeds. No significant difference was found

between the glucose concentrations at different mixing

speeds of a stirred tank for both feeding locations after 3

h of cellulosic hydrolysis. The glucose production was,

therefore, insignificantly affected by the mixing speed

within the tested range.

In addition, during hydrolysis, stirring or shaking in a

mixer tank is required to enhance the contact between

enzyme and cellulose particles and to increase the

mobility of enzymes throughout the entire volume

(Jorgensen et al., 2007; Mais et al., 2002). Product

inhibition by glucose and cellobiose at increased

concentrations at high solids loading plays a role for the

decreasing conversion (Kristensen et al., 2009).

Therefore, stirring in a tank helps avoid the areas with

high concentration of hydrolysis products (cellobiose

and glucose) that can inhibit the action of enzymes

(Jorgensen et al., 2007). However, high-stirring speed is

not recommended as it may result in enzyme

denaturation and deactivation by the high shear forces

(Cao and Tan, 2004; Tengborg et al., 2001).

The correlation between stirring and shaking speed

and the generation of hydrolysis products has been

studied previously, but in an experimental way using

shake asks or stirred tank reactor (Jorgensen et al., 2007;

Ingesson et al., 2001). Besides, prior studies have noted

that the mixing speed of a mixer did not significantly affect

the generation of hydrolysis products (Jorgensen et al.,

2007; Ingesson et al., 2001). Hence, the simulation

results obtained in this study matches those observed in

earlier experimental studies which indicated that the

coupled DAE-QMOM approach with hydrodynamic is

capable of predicting the hydrolysis process. A major

constraint in the enzymatic hydrolysis of biomass for

ethanol production is the cost of cellulase enzymes and

any strategy that can bring down the production cost of

cellulases can significantly reduce the cost of bio-ethanol

(Sukumaran et al., 2009). The ability of DAE-QMOM to

simulate the hydrolysis system rather than an

experimental test is beneficial in avoiding production

cost due to expensive enzymes, machines and energy.

Effect of Enzyme Feeding Location

Moreover, the influence of the enzymes feed locations to the mixing quality and its correlation to the production of sugars during hydrolysis process had been looked into. To do these, the mixing value and the hydrolysis yield were measured when the enzyme was injected at four different points inside the stirred tank. The COMSOL program package was used for the model simulation that incorporated reaction kinetics and fluid flow properties. In cellulosic hydrolysis process, several phenomena occurred simultaneously. First, the particles began to break and due to the velocity of the fluid, they moved clockwise in the reactor. The diffusion and the advection velocity had been accounted as the main factors that affected particle distribution in the tank.

Besides, it was known that the flow field in the

stirred tank had two main regions: The one around the

impeller, where most breakages occur and the outer

circle of the tank. Using visualization, a significant

vortex of the enzyme inside the tank was observed. The

system can be observed from the snapshots of the

concentration field at different feed injection locations

as shown in Fig. 5 and 6. Figure 5 visualizes the case

where the feeding enzymes were located in the outer

circle. Since the velocity had been rather slow at the

seeding point, the initial transport was almost isotropic

from the seeding point. It clearly showed that the

enzyme was still undispersed and was concentrated in

the outer circle of the reactor.

On the other hand, Fig. 6 shows the enzyme

distribution in the mixer when the feeding location was

in the inner circle. This feeding was in the faster velocity

field in the center of the mixer and was spread in an

azimuthal direction. It only took a few minutes more for

the enzyme to be almost homogeneously distributed in

the mixer. The enzyme was strongly dispersed due to the

mixing effect that the recirculation zones had on the

reactor. To sum up, higher localized concentration was

observed when feeding was at the outer circle, as

opposed to being almost uniformly spread throughout

the domain when the feeding was in the inner circle.

Meanwhile, Fig. 7 illustrates a sketch depicting the

differences in the feeding locations of enzymes in a

stirred tank reactor, i.e., the (1) outer circle, (2) inner

circle, (3) tip of the impeller and (4) on the impeller,

whereas Fig. 8 shows the MixingValue as a function of

time for different injection points of enzymes in the

mixer. MixingValue is the difference of the actual

concentration and the average concentration integrated

over the domain. The increase at early times had been

due to the inlet of the enzymes.


DOI: 10.3844/jmssp.2016..

Fig. 5. The feeding enzymes located in the outer circle. As time progressed, the enzyme was still undispersed and was concentrated

in the outer circle of the reactor

Based on Fig. 8, feed injection locations (3) and (4)

yielded similar results. It was observed that the

MixingValue curve for enzyme feed on the impeller had

a peak above both the outer and the inner circle. Besides,

the required time to reach equilibrium or homogenous

distribution throughout the domain had been the longest

for the enzyme feed on the impeller than in the outer or

inner circle. In other words, the slowest spreading

occurred when the feed injection was located on the

impeller blades. Another essential point was that the

enzyme feed injection location located in the inner circle

had the lowest peak and the shortest time to reach

equilibrium compared to the other two locations.

In a similar way, the evolution of glucose

concentration corresponding to the feed injection

location is shown in Fig. 9. The enzyme injection on the

impeller yielded the least glucose concentration,

followed by the outer circle. The highest glucose

concentration was obtained by feeding the enzyme in the

inner circle of the mixer. As time progressed, the enzyme

spread more in the reactor and hydrolysis qualitatively

increased in all cases. The glucose concentration

increased over time as expected due to the reactions on

the cellulose chains reacted by EG1 and CBH1 enzymes.

Besides, this phenomena indicated a correlation between

the MixingValue and the production of glucose for each

location. In the enzymatic hydrolysis of the cellulose

process, sugar productions go hand in hand with efficient

mixing between the enzymes and the cellulose

substrates. The outer circle was clearly worse than the

inner circle feeding location in the mixing process, but

better than the one on the impeller.


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Fig. 6. The feeding enzymes located in the inner circle. The enzyme was strongly dispersed due to the mixing effect that the

recirculation zones had on the reactor

Fig. 7. The sketch of injection points of enzymes at four monitoring locations (1), (2), (3) and (4) used to predict the mixing


DOI: 10.3844/jmssp.2016..

Fig. 8. MixingValue as a function of time at different injection point of enzyme.

Fig. 9. The evolution of glucose concentration corresponding to the feed injection location.

Lavenson et al. (2012) performed an experimental

study using Magnetic Resonance Imaging (MRI), a

cylindrical penetrometer and HPLC and reported that

the spatial homogeneity in the distribution of enzymes

(mixing quality) had a major influence on hydrolysis

rate. Besides, according to (Hodge et al., 2008), mass

transfer was a limiting factor in the decreased

production of cellulase enzymes. Meanwhile, as

explained by (Griggs et al., 2012b), predictive models

for the enzymatic hydrolysis of cellulose enabled an

improved understanding of the current limitations and

might have pointed the way for a more efficient


DOI: 10.3844/jmssp.2016..

utilization of enzymes in order to achieve higher

conversion yields.

On the other hand, the findings retrieved from this

study revealed that the feeding location of enzyme in a

stirred tank affected the mixing quality of the hydrolysis

process. Therefore, the location of enzyme feeding must

be chosen wisely to minimize diffusion limitations

without denaturing the enzymes (at a high shear rate).

Moreover, changing the feeding location from the outer

ring and on the impeller to the inner circle increased the

MixingValue. Hence, for a specific geometry of a stirred

tank, the best location to feed the enzyme to the biomass

suspension had been in the inner circle, close to the

impeller, but not on the impeller.

Conclusion

In this study, the enzymatic hydrolysis of cellulose in

a stirred tank reactor was modeled. The Griggs kinetic

model was extended by adding diffusion, advection and

hydrodynamics, which had a simultaneous effect on the

system. The flow led was obtained by solving the single-

phase Navier-Stokes equations with a standard laminar

flow. The population balance equation was solved

through the combination of Differential Algebraic

Equations and Quadrature Method of Moments (DAE-

QMOM). The DAE-QMOM was incorporated into an in-

house CFD code to simulate the enzymatic hydrolysis of

cellulose in a stirred tank reactor. Besides, numerical

simulation using 2-node QMOM indicated that the

results showed a good qualitative agreement with the

experimental results.

Hence, a DAE-QMOM approach was found to be

effective for PBE-advection diffusion model with the

incorporation of a CFD framework. This method had

been shown to provide reasonable predictions at a

reduced computation expense for a single-phase system.

In addition, this approach enabled one to get a better

understanding of the hydrolysis model as the owing fluid

had been taken into account as the environment in the

hydrolysis process. Besides that, further insight into the

mixing process was obtained by predicting the effects of

the mixing speed and enzyme feeding locations in the

mixer. The quality of mixing within the reactor is crucial

in optimizing the hydrolysis product. Moreover, the

results from this paper showed a qualitative agreement

with the experimental results obtained in previous studies.

In conclusion, the existing gap between PBE reaction

kinetics and Navier-Stokes equation for the enzymatic

hydrolysis of cellulose had been successfully bridged.

Acknowledgment

The author gratefully acknowledged the financial

support received from Universiti Malaysia Pahang

(RDU 150399).

Author’s Contributions

Norazaliza Mohd Jamil: Did the research, analysed

and interpreted the result, prepared the manuscript, and

responsible for the manuscript correction, proof reading

and paper submission.

Qi Wang: Designed the research plan and organized

the study, assisted in research work, provided the

intellectual input and designs in the study, and reviewed

it critically for significant intellectual content.

Ethics

This article is original and contains unpublished

material. The corresponding author confirms that all of

the other authors have read and approved the manuscript

and no ethical issues involved

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CFD-PBE Modelling and Simulation of Enzymatic Hydrolysis ... · Enzymatic hydrolysis of cellulose is a complex phenomenon. It consists of several effects that occur simultaneously